Internal problem ID [5714]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Section 4.5. More on Regular
Singular Points. Page 183
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 \left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = -1\).
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 43
Order:=8; dsolve(3*(x+1)^2*diff(y(x),x$2)-(x+1)*diff(y(x),x)-y(x)=0,y(x),type='series',x=-1);
\[ y \relax (x ) = \left (x +1\right )^{\frac {2}{3}-\frac {\sqrt {7}}{3}} c_{1}+\left (x +1\right )^{\frac {2}{3}+\frac {\sqrt {7}}{3}} c_{2}+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 42
AsymptoticDSolveValue[3*(x+1)^2*y''[x]-(x+1)*y'[x]-y[x]==0,y[x],{x,-1,7}]
\[ y(x)\to c_1 (x+1)^{\frac {1}{3} \left (2+\sqrt {7}\right )}+c_2 (x+1)^{\frac {1}{3} \left (2-\sqrt {7}\right )} \]